Modern data-driven technologies are providing us with new capabilities for work- ing with data across diverse storage architectures and analyzing it in unified frameworks to yield powerful insights. Even as the benefits of these technologies come into focus, they are fueling a corresponding debate over the responsible use of data and the urgency of mitigating privacy risks to individuals. This discus- sion is happening as new analysis techniques, based on correlating data across sources and types and exploiting statistical structure, have challenged classical approaches to privacy, leading to a need for radical rethinking of the meaning of privacy and its application to federated databases.